Answered

Give the equivalent numerator if the denominator is (x - 2)(x - 1)(x - 6).


2/(x-2)

Verified Answer :

JcAlmighty

The answer is 2(x - 1)(x - 6)

Let A be the equivalent numerator: \(\frac{A}{(x-2)(x-1)(x-6)}\)

If \(\frac{2}{x-2} =\frac{A}{(x-2)(x-1)(x-6)}\),
then: \(A = \frac{2(x-2)(x-1)(x-6)}{(x-2)}\)

(x-2) can be cancelled: \(A = \frac{2(x-2)(x-1)(x-6)}{(x-2)}= 2(x-1)(x-6)\)

Answer:

The required numerator is 2x²-14x+12 OR 2(x-1)(x-6)

Step-by-step explanation:

Considering the equivalent of the ratio of numerator and denominator to be 2/(x-2), we have to find numerator for given denominator.

Let numerator is A:

then:

\(\frac{2}{x-2}=\frac{A}{(x-2)(x-1)(x-6)}  \\\)

cancelling (x-2) from both sides:

\(2=\frac{A}{(x-1)(x-6)}\)

Multiplying numerator of A on left side:

\(2(x-1)(x-6)=A\\2(x^{2}-7x+6)=A\\2x^{2}-14x+12=A\)

Hence,

The required numerator is 2x²-14x+12 OR 2(x-1)(x-6)

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